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Thank you so much!!!

What is the value of (1 + i)^5 - (1 - i)^5?

Hello wiseowl!

\((1 + i)^5 - (1 - i)^5=\color{blue}-8i\)

  !

point slope form

(y - - 3) = -1/2 (x-2)

or   re-arrange to"

y = -1/2 x -2

A regular decagon is rotationally symmetrical by 360/10 = 36 degrees.

To take I to E, that rotation needs to be done 4 times, so alpha is equal to \(4(36)=\boxed{144}\)

Surface  area  = 

Area of  two right  triangles  with legs  of  3  and  4    =  3 * 4  =  12

Area of   three  rectangles  with  heights of 10  and widths of 3,4 and 5  =

10  ( 3 + 4 + 5)  =   10  ( 12)   = 120

Surface area  =  (12  + 120)  = 132 cm^2

Volume  =  Area  of  one right triangle * height of  10  =    6 (10)  = 60  cm^3

B  =  [  - 8 + (2/5) ( 2 - - 8)  ,   6  +  (2/5) ( 5  - 6)  ]   =

[ -8  + (2/5) (10) ,  6  + (2/5)(-1)  ]  =

[-8 + 4 , 6  -  2/5  ]  =

( -4 , 28/5)

Angle B = 1/2(360 - 100 - 96)

Isn't it just 10% ?

x   from  -8  to  2   is distance of 10      2/5 of this distance added to -8  =  -4

y              6 to  5   is a distance of -1    2/5 of this added to 6                 = 5 3/5

60% + 25% = 85 %       that means 15% were 'other'

.15(60) = 9  'others'

.....hmmmmm.....   not a right triangle....will not work....Pythag does not apply.....dang-o....

Factors of  -12    that when added = positive k    (note that k has a negative sign in front of it in the equation)

1   -12             added together = k  =   (-)   11

2     -6                                                  (-)     4

3    - 4                                                  (-)     1

example :   (x+1)(x-12) = x^2 -11x -12      k = 11

11 + 4 + 1 = 16

Find the longest side of a shaded triangle using the Pythagorean theorem.

Use the trig to find angels of a shaded triangle.

hi this is the same person who wrote the question is it correct that as if you do this process with any multiple of 101 you get 0 and as you can divide any number by 0 that is the answer?

The solution to the inequality is m < 8, so the largest integer that works is m = 7.

Let's check your work:

Small triangle         P₁ = 12  (3+4+5)         A₁ = 6

Large triangle         P₂ = 24  (6+8+10)       A₂ = ?         ? = 24

k = 24 / 12 = 2

A₂ = k² * A₁ = 24

Good job, Omi67!!!

2+sqrt(2)

Sorry the perimeter of the square is 2 + sqrt(2)

Two circles inside a square are externally tangent to each other and are tangent to certain sides of the square as shown.

The perimeter of the square is ????

It is a dome shaped parabola   so the  x^2   coefficient must be negative   so either   a or d

   at x = 0     a   will not work   but  d   does !      You got it correct !

If they have the same slope and y -intercept they are the SAME lines.....

Two triangles are similar. The smaller triangle has a perimeter of 2 units and an area of 2 square units. The perimeter of the larger triangle is 3 square units. What is the area of the larger triangle?

Area pf rectangle + area of triangle = total area

    10   x     8        +  1/2* 6 *8            = area  in  m²

Yes       2x^2 + x     is the same as   2x^2 + (1)(x)    BUT   x does not necessarily = 1

Ali, Clara, and Shan raised money for new books for the school library. Ali raised 20% more than Clara and $58 more than Shan. Clara raised 1/4 more than Shan.
A) How much money did they raise altogether
B) What percent of the total money did Clara raise?